A wormhole is a tunnel connecting two distant regions of the universe. If such a wormhole existed and were traversable, a particle inside it would feel not only gravity but also a force from its own electric field. This force depends on how spacetime is curved around it.
The authors took a wormhole model with two parameters: one sets the shape of the throat (how "flared" it is), the other sets the strength of tidal effects (how strongly it stretches objects). They placed a stationary charge inside such a wormhole and calculated the force acting on it. It turned out that the force is not always directed toward or away from the throat: it can change direction as you move away from the center. In some cases, there were two such "switches."
Another surprise: at large distances, the force falls off more slowly than in ordinary space. In flat space, the force from a charge drops as one over distance squared, while the self-force drops as the cube. Here, if the wormhole is sufficiently "red" (strongly slows time near the throat), the force can decay much more slowly. This means the particle senses the global shape of spacetime, not just the local curvature. Such behavior makes the self-force a sensitive probe for testing theories of gravity.
In the most extreme wormholes, the self-force decays just as slowly as in the famous Ellis wormhole, the simplest model without matter.
A similar tunnel appears in the movie Interstellar, where heroes fly through a wormhole in search of a new home.